Vibration mode analyzer



July 7, 1953 s. J. LoRlNG VIBRATION MODE ANALYZER' Filed July 11, 1946 l0 Il IN V EN TOR.

/e so 33 6 /5 sa ze 54 F15-E 44 AT TORNE Y Patented July 7, 1953 OFFICE vIBnATIoN MODE ANALYZER Samuel J. Loring, Stratford, Conn.

Application July 11, 1946, Serial No. 682,882

s claims. (cm3-67) This invention relates-to fnewand useful iml provements in means' for measuring vibration characteristics of structures and has particular relation to a vibration mode analyzer. 7

An object of the invention is to provide a vibration mode analyzer providing a simple'and direct means for measuring the natural frequency and Y l `having-a socket or opening 2I drilled or otherwise formed therein in eccentric relation tothe Y the nc'irmalA mode deection shapes and damping characteristics of structures. e Another object is to provide a self-contained instrument or device for the purpose stated and which is relatively small and of light Weight, requiring no 'outside power source,A and which is readily operated by one person. y

Other objects and advantages of the invention will become apparent from ya consideration of the means for securing the analyzer to the strucl ture or part Ill is generally designated I5 and p comprises a tubular body IB and lugs or feet Il the following detailed description taken in con- Y nection with the accompanying drawing wherein a satisfactory embodiment of the invention is shown. However, it is to be understood that the invention is not lirnitedto the details disclosed but includes all such variations and modifications as fall within the spirit vof the invention4 and the scope of the appended claims.

In the drawing: 1

Fig. l' is a View partly in partly in vertical section showing a device made in accordance with the invention; f 1 y Fig. 2 is a front elevational view of the device;

Fig. 3 is a top plan view thereof;

Fig. 4 is a detailed rear elevational View showing a suggested way in which the device may be mounted on a structure to be tested;

Fig. 5 is a side elevational view of the parts shown in Fig. ll; and

Fig. 6 is a iront elevational View illustrating a scale means employed. y

Referring in detail to the drawing, the device oi the invention is shown as including a supp-ort generally designated I!! and which latter includes an upper arm II, a lower arm I2, and a connecting portion I3 integral with said arms. Actually the support It is of somewhat the shape of the handle bars of a vbicycle or in the shape of a U arranged on one of its arms. The support, as shown, is formed by suitably bending up' a piece or metal tubing and comprises a very rigid structure ofv light weight. When the device of the invention is in use the support Ill is rigidly attached to the structure, the vibration mode of which is to beV analyzed.

In thedrawing, a portion of sucha structure is shown at Ill and this may be a part of a bridge, building, machine, airplane, or any other structure whichis to be analyzed. In the drawing,

side elevation and against the part U and a vertically extending arm I8 provided with a longitudinally extending slot I9.

Within the body I6 is ajplug-like device 20 longitudinal center thereof. ,Thus the part 2li has a taperedor bevelled wall and in the thinnest portion cf said wall is an enlarged opening 22 fromA one edge of which extends a slot 23. It will be appreciated that the opening 22 together with the slot 23 forms akeyhole opening.

The part 2d is disposed within the free end portion of the arm I2 of the support and a screw .24 passing through the body i6 enters a groove 2t in the part 2t whereby the opening 22 and slot 23 are ,aligned `with openings 26 and 2l through the bottoni wall of the body I6 and the bottom wall of the arm I2, respectively.'

with the described construction, when thek analyzer is to be attached to the structure I4, a screw or other means 2S is partly threaded into the said structure. Then the analyzer is Vdisposed ony the structure by aligning the openings 2d, 27 and 22 with the head of the screw and simply dropping the structure over such'head.

Thereafter, a wrench or other suitable tool is applied to the natted or lug-like portion 29 integral with the front end of part 20, and the latter is rotated so as to carry its opening 22 toward its upper side and to move its thickened wall portion under the head of the screw until a tight wedging action is accomplished, as suggested in Fig. 4. At this time the support I0 and all the parts carried by the latter will be rigidly attached to the structure It.

Suitableperforated lugs or loops 30 and 3l are attached to the inner sides of the arms Il and body I6, and, as shown, are attached by rivetllke Shanks 32, the heads of which are turned over at the inner sides of such arms.

C Dependlng from the loop SIB is av coil spring 33 and anchored at its lower end to theloop 3l is a coil spring 3Q. Thus, these coil springs are secured ed the inner nut-like portions 31 of a pair of de vices 38 and 39 respectively. Thus, the loading means is provided with or mounted by elastic restoring means and so is capable of linear vibrations. Y

In the actual structure. a pair of nuts 49 and 4I are threaded inwardly from the respective ends of the long screw 36. Next, the upper and lower rearwardly directed parallel arms 42 and 43 of a U-shaped indicator mounting means 44 are passed over the ends of the screw. Such mounting means, in addition to the arms 42 and 43, includes a connecting and face portion 45 of rela-.- tively large area.

Now the end portions 47 and 45 of the upper and lower guide means 49 and 50 are passed over the ends of the screw 36. Thereafter, the nut like portion 31 of the device Saris threaded onto the upper end of the screw and with the nut 40 serves to clamp the arm portions 42 and 41 another but are arranged in reversed' relation. i

Thus, guide 49A is made up ol?4 sheet metal and includes a nat body portion 53' having a pair of finger-likeportions 54 at its rear end bolted to lugs 55 on the sides of the connecting portion I3`of support $9. are designated 56, Additionally, guide 49 includes depending ange portions 51 along its longitudinal edges and a depending flange portion 58 between the portions 54. At its forward or outer end the guide also includes` the portions 4'I'previously referred to.

Guide includesiinger-like portions 59' corresponding with theportions 540i guide 49 and secured to lugs 55 as by bolts 56; Since the guide 50 isarranged in reverse relation to the guide 49, thesideor edge flangesV 6I and the end ange 621of1theV guide 59 extend upwardly or in the direction! of theguide 49 from a flat body portion 69. Bothv off these guides are formed of metal having-thecharacteristic of resiliency orv whichi'sspring-like. However, owing to the provision of-:the side flanges and the end flanges, itiwill'bea-pparent that the intermediate or main body portions of the guides are not flexible, but, on the contrary, are quiteV rigid.

However, while the guides areV rigid in their intermediate portions they are exgible and resilient or vibratable. in their respective fingerlikeportions 54 and 59. Such portions provide only for vibration of the guides in directions toward and from'. one another and toward and from thearms II and I2. That is, the'guides may vibrate in directions longitudinally of the screw 35. The guides maynot-vibrate laterally since they are each held' or mounted by two spaced nger portions and each in its intermediate*portionincludes a relatively' wide seat'- like body 53 on Y80.'

Later inthe description of the operation,l the manner of use of the present analyzer will be outlinedl but here it may be stated that in the use of the device, after it is attached to the structure to be analyzed, the loading means 35` is displaced longitudinally of the springs and,

then'released. I-vhave provided means whereby The bolts for this purpose f the weight may be successively released from a predetermined position of displacement.

As here shown, such means includes an opening or socket 63 formed in the spring attaching device 39 together with a plunger structure generally designated 64. This plunger structure includes a cylindrical body 65 having a reduced end portion E6 passing through the slot I9 of the arm I8 and threaded at its free end. A nut El is threaded to such end andy froml Fig. l it will be understood that on loosening of thisA nut, the entire assembly may be adjusted in the direction of the slot I9, to the desired position, and thenthe nut tightened to secure the assembly in this new position.

Extending longitudinally through the casing is a pin or plunger 68 normally held in the retracted position shown by means of a coil spring 69 disposed aboutV the plunger and at one end bearing against a head 10 of the plunger and the., other end against an internal wall ll, Complete withdrawal' of' the plunger or pin from the casing is prevented by engagement of" a shoulder 'l2 on the former with the wall 'il of the latter. A secondary guide means for the plunger or pin may be provided within thel casing, as shown, at T3;

After the assembly 64 has been adjusted along the slot I9, the loading means 35' may be displaced downwardly to alignthe socket 93 withv the freev or inner end of the pin 58V whenthe latter is pushed-into said socket. rlhis main',- tainsthe loading device 35 in-v a deiinte position of displacement and it will be understoodA that when this displacement takes place the spring 33 is further elongated andthe spring 34? is permitted to contract while the guides- 49' and.

50 are flexed downwardly. OnA releaseof thev hand pieceV or head 10, springv 69 retractsgthe` plunger orV pin withdrawing it from the socket;

53, permitting thel loading meansV to be snappedA upwardly by the spring 33' and setto vibrating upwardlyand downwardly between the arms II and I2'. Side or-lateral motion of the loading means is prevented bythe guidesY 49v and' 59, since the latter are not susceptible of such a motion.

rEhe elongated screw 36'01" the loadingl means is adapted to receive a test mass comprisingl a plurality ci weights, such as the relatively large weights 74 and then the very-thin weights-A 15, the latter being added experimentallyuntil the proper. mass issecured to the screw 35'. The test mass, of course, is a relatively small mass compared with the mass of the structure being tested. A binding nut 'i6 isk provided for securing the weights rigidly in place and against any free movement independent of the screw 35. be understood that the Yweights are vpreferably of the type having a slot passing' through an edge' Y and the loading means displaced.andreleased.

Asthe loading means is-displac'edA and released,

it will it vibrates and carries a chart ory scale 11, at-

I dotted line shown at 19a indicating one possible point of appearance of the illusion. The operator determines the amplitude ofvioration of the dcvice by observing' the movement of the indicator i9 or the distance between the two indicators seen because of the optical illusion, or the lateral depth of the spacebetween the real and the imagined indicator.

The nature and interpretation of the indications of the instrument are best described analytically in terms of the following quantities, the signicance of which will be apparent to those skilled in the art:

No==natural frequency in cycles per second of Y loading means with all its attachments on springs 33 and 3d and guides le and Eil.

Ns=natural frequency in cycles per second of structure iii being tested. Y

mo=efective moving'mass of loading means 3&3

with all its attachments.

ms=effective mass of structure I4 in its naturai .vibration mode at point of attachment of frame i6. y0=effective damping factor of motion of loading ymeans 35 with all its attachments, measured as the effective fraction of the elastic restoring force which acts 90 out of phase with its motion. gs=efiective damping factor of structure is in its natural mode of vibration, 'and measured in the same manner as go. Y r=ma,/im=ratio of effective mass of loading means 35 with all its attachments to effective n mass of structure ill. G=(gs-ga)/2\/17=dimensionless parameter further characterizing relation of vibration characteristics of loading means y35 and all its attachments, and structure i4. n A=amplitude of vibration of loading means 35 with alldits attachments. Tv=7TNo'\/T.

When my device is used in the preferred manner it is attached to a structure which'is not vibrating due to. any externally applied forces. Small vibrations of the structure are actually introduced by theforces attending the motions of the loading means 35 following its initial release from a displaced` position. My device thus acts as a means for exciting small vibrations of a structure being tested as well as a means for measuring the signiiicant features of the vibratory response of the structure to this excitation. The formulae hereinafter given for interpreting the motions of the loading means 35 subsequent to its release apply specifically to this preferred use of my device. It will, however, be apparent to those skilled in the art that similar, but not identical characteristic motions of the loading means 35 would result if vibrations of the structure were excited by some other force or impact applied at any other point of the structure, and that these characteristic motions could also be used to deduce the general vibration characteristics of the structure. f

Y When the frequency No is not close to the natural frequency N5 of the structure I4 being tested, the motion of the'loading means 35 subsequent to its release from a displaced position has an amplitude which may be read visually on the indicator `il and which subsides with time t as indicated in the equation:

However, when the frequencyNo isjust equal to Ns the vibratory motion of loading means 35 subsequent to its release has an amplitude (which again may be observed visually on indicator Ti) which Varies accordingto a more 'complex law which is very decidedly influenced by the specific `Vibration characteristics ms and gs of the structure i4. This law is as follows: When The responses (represented by formulas 2a, 2b

yZcindicate that the amplitude of vibration will decrease with time more rapidly than would be the casefror the motion corresponding to Formula 1.

In determining the natural frequency civ a structure, the frame lil is attached to the structure and the loading means displaced andreleased so that its vibrations can be observed. This is done successively with a series of weight combinations on the loading means so as to produce a set of Yclosely spaced natural frequencies ofthe loading means. rlhe course of variation of amplitude of the loading means will, in most cases, correspond to Formula 1. However, when the natural frequency of the loading means becomes equal to a natural frequency of a structure on which the instrument Visy mounted, one

with time to one ofthe Formulas 2a, 2b or 2c by adjusting the parameters 1' and G in these formulas vfor best t. It will be apparent to those v skilled in the art that vthere are many simple procedures'for carrying out such a step.

The natural frequency of the structure Ns is equal to the value of No at which responses of the type (2a, b, c) are observed. A study of the actual response shape leads, by comparison with the various shapes implied by equations (2a, b, c) to a quantitive determination of the parameters 1 and G .from which may be deduced the vibra= tion characteristics ms and gs of the structure ld.

The transition from a response of type (2a, b, c) to type represented by Formula 1 takes place in a relatively narrow frequency range of No, usually within a variation of 2 to 5%. The instrument is capable, therefore, of isolating natural frequencies of a structure which lie relatively close together. A study of relations (2a, b, c) will show that the vibration characteristics of structures for which r has the range 1./100 to l/l00,GOQ, and G the range to l0 are readily observable.

Those skilled inthe art will recognize that the reciprocal of the square root of the eifective mass oi a point of structure in a natural mode may be identified with the deflection of that point in the natural mode. Therefore, by making observations at a number. of points of a structure the shape of the deflection curve in the natural vibration mode may be determined.

Having thus set forth the nature of my invention, what I claim is:

l. In an apparatus for the purpose set forth, a support including a pair of spaced rigidly connected substantially aligned upper and lower arms, upper and lower elastic means connected with the respective arms, a loading means, said elastic means connected with said loading means whereby on release of the latter following displacement thereof toward one of said arms it will,

vibrate back and forth between the arms, means for securing various weights to said loading means, meansV for holding said loading means in a predetermined position of displacement and for releasing it from such position whereby the loading means may he repeatedly released from the same position of displacement, a scale movable with said loading means Yand including a series of spaced vertical lines, a pointer on and movable with said scale and extending across said lines, said scale and pointer adapted to vibrate with said'loading means whereby through an op-= tical illusion said pointer will appear to occupy two positions with respect to said lines while the loading means is vibrating and the apparent two positions of the pointer with respect to the vere tical lines forms the basis for determining the amplitude of vibration of a structure to which the apparatus may be attached, and means for rigidly engaging said apparatus with an object the vibration characteristics of which are to be determined.

2. In an apparatus for the purpose set forth, a rigid support, a loading means, elastic restoreing means mounting said loading means on said rigid support whereby the loading means is capa= ble of linear vibrations relative to the support, said yloading means comprising a rigid element elongated to have various weights-stacked one on another thereon, means on said element and ad- .instable therealong for rigidly clamping said various stacked weights to said element against movement relative thereto and relative to one another, and means for rigidly attaching said rigid support to a structure the vibration characteristics of which are to be determined.

3. In an apparatus for the purpose set forth, a rigid support, a loading means, elastic restoring means mountingA said loading means on said rigid support whereby the loading means is capable of linear vibrations relative to the support, means for securing various weights to said loading means, releasable mechanical means mounted on said support and engageable with said loading means for positively locking said loading means in a predetermined position of adjustment when moved thereto, and means for rigidly attaching said rigid support to a structure the vibration characteristics of which are to be determined.

4. In an apparatus for the purpose set forth, a rigid support, a loading means, elastic restoring means mounting said loading means on said support whereby the loading means is capable of linear vibrations relative to said Support, means for securing various weights to said loading means, releasable mechanical means mounted on said support and engageable with said loading means for positively locking said loading means in a predetermined position of displacement when moved thereto, guide means comprising a pair of parallel arms anchored at their respective end portions to said rigid structure and said loading means and iiexible in the direction of said linear vibrations, said arms intermediate their an.- chored respective end portions of channel formation in transverse section whereby they are rigid in all other directions and thereby limit the path of vibration of said loading means, and means for rigidly attaching said rigid support to a structure the vibration characteristics 'of which are to be determined.

5. In an apparatus for the purpose set forth, a support including a pair of spaced rigid arms and a rigid portion connecting said arms, an elongated loading means located between said arms to have various weights stacked one on another thereon, means threaded on said elongated loading means and threadable therealong to rigidly clamp said various stacked weights against relative movement and against movement relative to said elongated loading means, an elastic means connected at its respective ends to one of said arms and to one end of said loading means, a second elastic means connected at its respective ends to the other of said arms and the other end of said loading means whereby the latter is mounted for movement and will vibrate relative to said arms when displaced and released, and means on one of said for rigidly attaching said apparatus to an object the vibration characteristics of which are to be determined.

d. In an apparatus for the purpose set forth, a support including a pair of spaced rigidly connected substantially aligned arms, an elongated loading means located between said arms, an elastic means connected at its respective ends to one of said arms and one end of said loadingmeans, a second elastic means connected at its respective ends to the other of said arms and the other end of sai-i loading means whereby the latter is mounted lfor movement and will vibrate between said arms when displaced and released, means for clampingly securing various weights on said loading means, a stiif, visually observable indicator means comprising an arrow-shaped pointer at right angles to the path of movement of the loading means and iixed to and movable with said loading means to indicate the amplitude of vibration thereof, and means for rigidly engaging said apparatus with an object the vibration characteristics of which are to be determined.

7. In an apparatus for the purpose set forth, a support including substantially aligned upper and lower arms and a rigid connecting portion rigid with said arms, upper and lower elastic means connected with the respective arms, a loading means, said elastic means connected at their inner ends with said loading means whereby onrrelease of the latter following displacement thereof toward one of said arms it will vibrate back and forth between the arms, guide means comprising a pair of parallel guide arms anchored at their respective end portions V-to said connecting portion of the support and said loading means and flexible only in directionsltoward and from said arms, said parallel guide arms `intermediate their anchored respective end portions of channel formation in transverse section whereby they are rigid inrall but said back and forth directions and thereby limit said back and forth vibrations to a predetermined path, means for securing various weights to said loading means, releasable mechanical means mounted on said support and engageable with said loading means for positively locking said loading means in a predetermined position of displacement when moved thereto, and means for rigidly engaging said apparatus with an object the vibration characteristics of which are to be determined.

8. In an apparatus for the purpose set forth, a rigid support, a loading means, elastic restoring means mounting said loading means on said rigid support whereby the loading means is capable of back and forth linear vibrations, means 10- limiting the vibrations of said loading means to substantially a fixed path, means for securing various weights to said loading means, a post extending along said path, releasable mechanical means mounted on saidpost for positively locking'said loading means in a predetermined posi- VVtion of displacement when moved thereto, means mounting said locking means on said post for adjustments longitudinally of the latter, and means for rigidly attaching said rigid support to a structure the vibration characteristics of which are to be deterimned.

SAMUEL J. LORING. 

